Vector Dot (Inner) Product Calculator

An online calculator for finding the dot (inner) product of two vectors, with steps shown.

$$$\mathbf{\vec{u}}$$$: (
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$$$\mathbf{\vec{v}}$$$: (
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Hint: if you have two-dimensional vectors, set the third coordinates equal to or leave them empty.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Calculate $$$\left(7, 0, -2\right)\cdot \left(1, -1, 4\right)$$$.

Solution

The dot product is given as $$$\left(u_{x}, u_{y}, u_{z}\right)\cdot \left(v_{x}, v_{y}, v_{z}\right) = u_{x} v_{x} + u_{y} v_{y} + u_{z} v_{z}$$$.

Thus, what we need to do is to multiply the corresponding coordinates and then add up the results: $$$\left(7, 0, -2\right)\cdot \left(1, -1, 4\right) = \left(7\right)\cdot \left(1\right) + \left(0\right)\cdot \left(-1\right) + \left(-2\right)\cdot \left(4\right) = -1.$$$

Answer

$$$\left(7, 0, -2\right)\cdot \left(1, -1, 4\right) = -1$$$A